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Table of contents

  1. Front Matter
    Pages i-xix
  2. Philippe Robert
    Pages 1-27
  3. Philippe Robert
    Pages 29-56
  4. Philippe Robert
    Pages 57-77
  5. Philippe Robert
    Pages 79-101
  6. Philippe Robert
    Pages 103-140
  7. Philippe Robert
    Pages 141-175
  8. Philippe Robert
    Pages 177-206
  9. Philippe Robert
    Pages 207-229
  10. Philippe Robert
    Pages 231-278
  11. Philippe Robert
    Pages 279-302
  12. Philippe Robert
    Pages 303-329
  13. Philippe Robert
    Pages 331-350
  14. Back Matter
    Pages 351-399

About this book

Introduction

Queues and stochastic networks are analyzed in this book with purely probabilistic methods. The purpose of these lectures is to show that general results from Markov processes, martingales or ergodic theory can be used directly to study the corresponding stochastic processes. Recent developments have shown that, instead of having ad-hoc methods, a better understanding of fundamental results on stochastic processes is crucial to study the complex behavior of stochastic networks.

In this book, various aspects of these stochastic models are investigated in depth in an elementary way: Existence of equilibrium, characterization of stationary regimes, transient behaviors (rare events, hitting times) and critical regimes, etc. A simple presentation of stationary point processes and Palm measures is given. Scaling methods and functional limit theorems are a major theme of this book. In particular, a complete chapter is devoted to fluid limits of Markov processes.

Keywords

Applied stochastic calculus Ergodic theory Fluid limits M/M/1 queue Martingale Poisson process Queueing models Scaling methods Stochastic networks Stochastic processes biased random walk hitting time jump process stochastic network stochastic process

Authors and affiliations

  • Philippe Robert
    • 1
  1. 1.Domaine de VoluceauINRIALe ChesnayFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-13052-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-05625-3
  • Online ISBN 978-3-662-13052-0
  • Series Print ISSN 0172-4568
  • Buy this book on publisher's site